Here is the worlds easiest DIY earring tutorial, you really can make these in the time it takes to boil a kettle and all you need is some earring backs, strong glue and some flat backed gem stones. If you are new to DIY or a bit intimidated then these are a great place to start and don't require any additional tools. If you mount them onto pretty card or put them into a nice box they would make a great gift and are easy on the purse.
There are only two steps
1) Apply a dot of glue to the back of your gem, and leave to dry for a minute
2) Apply your earring back to the glue and leave to dry completely
Here are some more examples of what you can use for your earrings; to start you will need some earring backs this site does a great selection in both gold and silver. I don't like to go too big with my studs so stick to shapes which are around 1.5cm in width. I have made earrings using these porcelain flowers, but you can use anything as long as it has a flat back like these gemstones or cabochons, I like the look of these ones but search places like Ebay and Etsy for cute vintage alternatives. A word of warning, I would avoid using buttons or anything too old-lady-craft-fair as my idea of hand-made should be stylish not stuffy but thats just my opinion so as long as you are making it doesn't really matter.